An electrodynamic motor includes a magnet assembly that generates a constant magnetic field in a magnetic air gap and the voice coil immersed in the gap. An alternating current corresponding to electrical signals conveying audio signals interacts with the constant magnetic field. This interaction results in the Laplace force F, expressed as a product of the magnetic flux density B, the overall length of the voice coil's turns linked to the magnetic flux l, and the value of the electrical current running through the voice coil i, F=Bli. Due to the Laplace force acting on the voice coil wire positioned in the constant magnetic field, the alternating current actuates the voice coil to move back and forth in the magnetic air gap and, correspondingly, move the diaphragm to which the coil (or coil former) is attached. Accordingly, the reciprocating voice coil actuates the diaphragm to likewise reciprocate and, consequently, produce acoustic signals that propagate as sound waves through air.
Typically, the product Bl (called the force factor) is a function of the voice coil position in the voice coil gap: Bl(x), as shown in FIG. 1. The typical dependence of the Bl-product on displacement is essentially that of a soft limiter and remains almost constant at low levels of signal, thus producing minimum nonlinear distortion. In addition, the voice coil inductance is a function of the voice coil's position and it also depends on the instantaneous value of the current: Lvc(x, i), as shown in FIGS. 2 and 3, respectively, even at very small levels of signal. These latter two nonlinear parameters are major sources of nonlinear distortion in an electrodynamic loudspeaker. When the voice coil is in the inward position, it is surrounded by steel parts of the motor and its inductance is higher compared to the outward protruding position when part of the voice coil is surrounded by air. When the high-level current runs through the voice coil, it may saturate parts of the steel adjacent to the voice coil. Saturated steel has lower magnetic permeability and therefore the voice coil inductance decreases.
In general, operation of an electrodynamic loudspeaker is described by two nonlinear ordinary differential equations (W. Klippel, “Measurement of Large Signal Parameters of Electrodynamic Transducer”, presented at the 107st Convention of the Audio Engineering Society, preprint 5008, September 1999).
One of the equations describes the balance of forces:
                                          Bl            ⁡                          (              x              )                                ⁢          i                =                                            m              ms                        ⁢                                                            ⅆ                  2                                ⁢                x                                            ⅆ                                  t                  2                                                              +                                    R              ms                        ⁢                                          ⅆ                x                                            ⅆ                t                                              -                                    1              2                        ⁢                                          ⅆ                                                      L                    vc                                    ⁡                                      (                                          x                      ,                      i                                        )                                                                              ⅆ                x                                      ⁢                          i              2                                +                                                    K                ms                            ⁡                              (                x                )                                      ⁢            x                                              (        1        )            
where mms is the moving mass, Rms is the mechanical losses, and Kms(x) is the suspension's mechanical stiffness.
The second equation describes the balance of voltages for the case when the loudspeaker is driven by an amplifier with negligibly small output impedance, where Rvc is the simple resistance and Lvc is the ideal inductance that does not depend on frequency:
                    U        =                                            R              vc                        ⁢            i                    +                                    Bl              ⁡                              (                x                )                                      ⁢                                          ⅆ                x                                            ⅆ                t                                              +                                                                      L                  vc                                ⁡                                  (                                      x                    ,                    i                                    )                                                            ⅆ                x                                      ⁢                                          ⅆ                x                                            ⅆ                t                                      ⁢            i                    +                                                    ⅆ                i                                            ⅆ                t                                      ⁢                                          L                vc                            ⁡                              (                                  x                  ,                  i                                )                                                                        (        2        )            
As it follows from the equations (1) and (2), the nonlinearities coming from the terms Bl(x) and Lvc(x,i) are dominant. It is important to minimize dependence of these parameters on displacement and current.
In reality, the impedance of a loudspeaker voice coil does not only contain a simple resistance Rvc and an ideal inductance Lvc. Since the voice coil is surrounded by ferromagnetic and conductive materials, the voice coil impedance also incorporates magnetic losses and eddy currents. Thus, the ideal inductive element ZL=jωLvc should be replaced by the complex and frequency dependent element:ZL=Reff(f)+jωLeff(f)   (3)
where Leff is the frequency dependent inductance and Reff describes the electrical and magnetic losses due to the material surrounding the voice coil.
There are various existing methods that attempt to linearize the Bl-product and the voice coil inductance. The most popular methods are using either an overhung voice coil or an underhung voice coil (Gander M, J. Audio Eng. Soc., vol. 29, pp. 10-26, 1981, January/February). With an overhung voice coil, the electrodynamic linkage occurs only in a small part of the voice coil. With an underhung voice coil, the linkage is provided in a small part of the top plate and pole piece. Another prior method includes the use of an uneven winding of the voice coil (Olson H, Van Nostrand Reinhold, 1972, pp. 23-25; Mazin V and Sang Lee Y, 116th AES Convention, preprint 6152, 2004, Berlin). This method requires more turns at the peripheries of the voice coil, and also requires a wider gap to accommodate extra layers of peripheral turns and more complexity in fabricating the voice coil. Another prior approach is proposed in U.S. Pat. No. 7,283,642, wherein the underhung voice coil and the top plate and pole piece have cavities. The cavities are positioned against the central position of the voice coil. However, as the voice coil moves out of the gap, the Bl product remains flat because the loss of the magnetic linkage is compensated by the increased induction B.
One method to minimize variation of the alternating magnetic flux produced by the voice coil, and correspondingly, to minimize the voice coil inductance value at a zero position, as well as to minimize the dependence of the voice coil inductance on the coil's position and current involves implementing a selected conducting element. For example, conductive plating may be provided on a pole piece, a conductive cap may be provided over the pole piece, and a conductive ring may be used (Gander M, J. Audio Eng. Soc., vol. 29, pp. 10-26, 1981, January/February). The conductive elements act as a single-turn secondary winding of a transformer. The alternating current generated in the “secondary” turn produces an alternating current. This current generates an alternating magnetic flux opposite in sign to the flux generated by the voice coil and therefore decreases it. Such methods may be directed to minimizing the voice coil dependence on current and may decrease the absolute value of the inductance. However, they may not improve linearity of the voice coil inductance as a function of displacement.
An alternative approach to minimize variation of the voice coil alternating flux is using active compensation (Carlisi M et al., 118th AES Convention, preprint 6421, 2005, Barcelona). In this method, instead of using a single-turn conductive element, a multi-turn stationary coil is used. It makes possible various ways of driving the secondary coil, such as driving it with an additional amplifier, driving it in parallel with the voice coil from a single amplifier, driving it through the filter that shapes the driving level with the frequency, and simply shorting the stationary coil.
The nonlinearity that distorts a signal at its low levels is especially detrimental to the audible sound quality. Therefore, it is important to keep the “linear” value of the voice coil inductance as well as its variation on displacement and current low to minimize the flux modulation and to decrease the high-frequency attenuation cause by the impedance's inductive component.